Written by DECLAN WALSH, RICK LYMAN and MICHAEL D. SHEAR, The New York Times

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JOHANNESBURG — President Obama arrived in South Africa on Friday evening, saying he was bearing a message of “profound gratitude” to Nelson Mandela, the stricken former leader, and that he would defer to Mr. Mandela’s family on whether to visit him.

After an eight-hour flight, Air Force One landed at Waterkloof Air Base, just a few miles from the Pretoria hospital where Mr. Mandela has been under intensive care with a serious lung infection for nearly three weeks, as concerns about his health have intensified in recent days despite government assurances that Mr. Mandela’s condition had stabilized.

Mr. Obama’s plane left from Dakar, Senegal, the first stop on his Africa trip, where Mr. Obama met with farmers and entrepreneurs seeking enhanced food security through new agricultural practices and technology.

Speaking to reporters traveling with him aboard the flight, Mr. Obama said he had no further information on the health of Mr. Mandela, the 94-year-old icon of the successful anti-apartheid struggle in South Africa. Mr. Obama said that any possibility of a visit by himself, the first lady, Michelle Obama, and their two daughters would rest with the family of Mr. Mandela, who has been hospitalized since June 8.

“I don’t need a photo-op, and the last thing I want to do is to be in any way obtrusive at a time when the family is concerned about Nelson Mandela’s condition,” Mr. Obama said, according to a transcript of his remarks released by the White House. “I’ve had the opportunity to meet with him, Michelle and the girls had an opportunity to meet with him. Right now, our main concern is with his well-being, his comfort, and with the family’s well-being and comfort.”

Mr. Obama said the main message he intended to deliver to Mr. Mandela, “if not directly to him but to his family, is simply our profound gratitude for his leadership all these years and that the thoughts and prayers of the American people are with him, and his family, and his country.”

As supporters of the governing African National Congress party rallied outside the hospital in the capital, Pretoria, where Mr. Mandela was being treated, concerned relatives, clergy members and senior government have been streaming in to see Mr. Mandela, South Africa’s former president.

Although the government noted a deterioration in Mr. Mandela’s condition on Wednesday night, President Jacob Zuma offered modest reassurance after a visit on Thursday, relaying medical reports that Mr. Mandela, still critically ill, was “now stable.”

It was the latest in a series of official and unofficial assessments that have produced trepidation among Mr. Mandela’s legions of supporters across the world. In an interview with the state broadcaster, Mr. Mandela’s eldest daughter, Makaziwe Mandela, described his condition as “very critical” and warned, “Anything is imminent.”

“I won’t lie,” she added. “It doesn’t look good.”

Speculation about Mr. Mandela’s health, which has deteriorated since he was admitted to Mediclinic Heart Hospital with a serious lung infection almost three weeks ago, continued on Twitter and other social media, and spilled into some local news reports.

The alarms began sounding late on Wednesday, when Mr. Zuma abruptly canceled a visit to neighboring Mozambique, and later visited Mr. Mandela in the hospital for the second time in just over 12 hours.

In the Soweto section of Johannesburg on Thursday, a line of television cameras stood across the street from the Mandela House museum, where Mr. Mandela lived before his incarceration in the notorious Robben Island prison. A pair of musicians — a young woman on bongos and a man on guitar — played the same tune, over and over, and sang the same words again and again, “Nelson Mandela, Nelson Mandela, Nelson Mandela.”

The Rev. Thami Ntongana, a Nazarene minister, said he had been asked by the local African National Congress Youth League to lead a prayer and was waiting for a procession from a nearby church to arrive before he began.

“My prayer will be, ‘God, your will be done,’ ” he said. “We are sad about the situation, but we are realistic about it. We want Mandela to go in his own time, when the moment has come, and it is only God who can pull the main switch.”

In another section of Soweto, called White City — because it was one of the first sections to get electricity and so was bright white after dark — two young men sat at a curbside with a sign reading “Pray for Madiba,” a reference to Mandela’s clan name, by which he is widely known in South Africa.

“All we can do is wait and see now,” said Jabu Mkwele, 21, a taxi van driver when he can find work. “Madiba will go in his own time, and we must be strong and let him go.”

Although the effect of Mr. Mandela’s illness on Mr. Obama’s visit was not clear, his stay in South Africa is likely to be overshadowed by expressions of disappointment and even anger over his conduct in office.

While South African government officials promise an appropriately warm welcome, a coalition of trade union groups and left-wing political organizations is planning a “national day of action” on the first day of his visit, including a march on the American Embassy in Pretoria. The next day, student groups intend to protest outside the Soweto campus of the University of Johannesburg, where Mr. Obama is to receive an honorary degree.

Meanwhile, two national groups, including the Muslim Lawyers Association of South Africa, have urged the South African government to arrest Mr. Obama when he lands, accusing him of “war crimes, crimes against humanity and genocide” for the American drone attacks in Pakistan and elsewhere and for keeping the Guantánamo Bay prison in Cuba running.

“When President Obama was ushered into the world, there was a promise for change of policy, like the closure of Guantánamo Bay, and how he is going to respond to the dispute between Israel and Palestine,” Phutas Tseki, the regional chairman of the Congress of South African Trade Unions, said in announcing his group’s participation in Friday’s protests. “Now he is on his second term, and he continues to be arrogant, and his policies continue to entrench American power to the whole globe without any change.”

Asked to comment on the planned protests, Benjamin J. Rhodes, the deputy national security adviser, said only that South Africa “is a vibrant democracy.”

The scope of the protests indicates that the country’s longstanding skittishness about American foreign and trade policies has overridden its brief elation over the election of the first black president in the United States.

“The excitement that accompanied his historic 2008 election has given way to widespread cynicism on the continent,” Mwangi S. Kimenyi, a senior fellow at the Brookings Institution, said in a blog post at ForeignPolicy.com.

As he walked across campus on way to yet another meeting, Masete Levy, president of the University of Johannesburg’s student council, echoed that sentiment, saying that the students he represents are deeply disappointed by the gap between Mr. Obama’s promises as a presidential candidate and his actual policies in office.

“There is now among the students a feeling that Obama has done nothing to the advantage of South Africa, and has only continued the American policies around the world that we thought he was going to end,” Mr. Levy said. “He is a visitor of our government, and we do not object to that, but we do object to his being honored by our university and we want to make sure he hears our calls that he follow through on the promises he made.”

The South African government says it is welcoming the protests but will not allow them to derail the president’s visit. The protests “might have a positive effect,” said Clayson Monyela, a spokesman for the Ministry of International Relations. “It is a tangible demonstration of the healthy democracy we enjoy.”